Personally, my life is significantly better in the UK. I grew up in the US with family and friends all over and it's likely very region specific for both countries so a person can likely find a place there that they love just as much as they could find it in the UK. The only things I miss though as familiar forests I used to walk a lot in and certain comfort foods & sometimes it's annoying when certain products are US-only or online spaces are US-dominate; however, I would happily never see the US again whereas I would miss the UK very much.
I'm not sure how child well-being will be better in the US when it's significantly lower on most markers for areas related to that. Personally, having been the child stuck in a side room of an ER for hours alone because no one could get hold of my parents to get insurance information (I was stable but they wouldn't do further care without it) and the parent who had my child at camp taken to A&E and gotten all the care he could want before they called me, the idea of my kids being stuck in the situations I was in repeatedly as a kid terrifies me. To me, having lived in it so long when I was most vulnerable, it feels so risky in comparison even with all that is happening with the NHS now.
Just as in the UK you can have two schools in walking distance that are worlds apart, the same is true in the US so again it's a matter of checking your area carefully first when it comes to opportunities available as they can widely different within a few miles. I finished school in a city and some schools had vocational options or links to vocational centers or links to local universities to take courses there and some within the same area didn't. Personally, I hated how much of my school life, especially the high schools I went to, was dominated by sports teams; however, it is true on average that I've seen that US schools have more sports and activity options in comparison to the UK where most of those things are done outside of school which does have its own pros and cons and barriers.
Both countries have the issue where school requirements can change very quickly. When I finished high school literally the grade before me, my grade, and the grade after me had different requirements so sometimes you can check and things change. Overall, as I said, I think you can find somewhere in either that would be great for you and a family, but at the same time both have risks and barriers that can make things very unhappy.